Michael Cates University of Cambridge

##### Informatic versus Thermodynamic Entropy Production in Active Systems

Stochastic thermodynamics connects the steady-state entropy production rate (EPR) of a system connected to a heat bath with the log ratio of probabilities of forward and time-reversed trajectories. Extending the resulting formula to coarse-grained models of systems much further from equilibrium, such as schools of fish or herds of wildebeest, results in an informatic EPR (IEPR) that depends only on order parameter dynamics and is no longer is connected with microscopic heat flow, but remains a valuable quantifier of macroscopic irreversibility. When the same coarse-grained models describe more microscopic processes (such as active phase separation within a biological cell), a connection to heat flow should be recoverable. To achieve this we can embed the coarse-grained model into a larger model involving explicit (if schematic) chemical reactions such that the whole system is governed by linear irreversible thermodynamics. All the active terms in the order parameter dynamics then become off-diagonal elements of an Onsager matrix whose symmetry determines the remaining chemical couplings and thus the full heat production. This exceeds the IEPR by a term that contains complementary spatial information to the IEPR itself.

Video of the lecture